Theorems · Theorem · general topology
exists_isCompact_superset_iff
∀ {X : Type u_1} [inst : TopologicalSpace X] [R1Space X] {s : Set X}, (∃ K, IsCompact K ∧ s ⊆ K) ↔ IsCompact (closure s)- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceR1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsCompactstatement and proof · cited by 1,282
- closurestatement and proof · cited by 1,254
- subset_closureproof · cited by 309
- R1Spacestatement and proof · cited by 125
- IsCompact.closure_of_subsetproof · cited by 15
Cited by1
Results whose statement or proof uses this declaration.
- exists_compact_iff_hasCompactSupportproof · cited by 3